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" In any triangle the square on a side opposite to an acute angle is less than the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum... "
A new supplement to Euclid's Elements of geometry, by the author of 'A new ... - Pagina 56
door Joseph Denison - 1840 - 84 pagina’s
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Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

Daniel Adams - 1849 - 128 pagina’s
...inscribed square. III. Add the squares together, and extract the square root of their sum. NOTE. The side of a hexagon inscribed in a circle is equal to the radius of the circle. EXAMPLES FOR PRACTICE. 1. The radius of a circle is 5 inches; what is the side of its...
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mensuration mechanical powers and machinery

1850
...inscribed square. III. Add^the squares together, . and extract the square root of their sum* NOTE. The side of a hexagon inscribed in a circle is equal to the radius of the circle, EXAMPLES FOR PRACTICE. 1. The radius of a circle is 5 inches ; what is the side of its...
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Hermathena, Volume 4

1883
...which are larger or smaller than semicircles contain, respectively, acute or obtuse angles ; (c). The side of a hexagon inscribed in a circle is equal to the radius ; (d}. In any triangle the square on a side opposite to an acute angle is less than the sum of the...
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Greek Geometry from Thales to Euclid

George Johnston Allman - 1889 - 237 pagina’s
...which are larger or smaller than semicircles contain, respectively, acute or obtuse angles ; (c). The side of a hexagon inscribed in a circle is equal to the radius ; (). In any triangle the square on a side opposite to an acute angle is less than the sum of the...
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The NAEP ... Technical Report

1972
...is Euclid III. 31, although there is some evidence that the earlier proofs were different.)32 3. The side of a hexagon inscribed in a circle is equal to the radius (IV. 15, porism). He knew how to solve the following problems: (1) about a given triangle to describe...
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